The plot of Devil May Cry follows the Demon Hunter Dante, the son of a legendary demon who seal off the demon world named Sparda and a human named Eva.
Games of the original series (in chronological order of it's events)
Devil May Cry 3: The prequel to the series. It starts with an 18 year old Dante starting his small mercenary business when a man named Arkham comes and tells him of an invitation from his brother, Vergil. Dante accepts (In a way) and begins his quest to stop his brother from breaking the seal their father place and unleashing Hell on the Human realm threw the demonic tower Temen-ni-gru. Along the way he meets Lady, a young woman with connections to Arkham.
Devil May Cry: The first game of the series, takes place sometime after Devil May Cry 3. Dante, now older, has established his business but gets a rude house guest. A demon named Trish attacks Dante and informs him that the Dark Lord Mundus has awakened from being previously sealed by Sparda and now seeks to reunite the Human Realm and the Demonic Realm as one just like it once was (See Code 1: Dante). Dante spares her due to her resemblance to his deceased mother and travels with her to Mallet Island and battles Mundus's generals on a quest for revenge against the Dark Lord.
Devil May Cry: The Animated Series: During the events that took place after Devil May Cry and before Devil May Cry 2, Dante is charged with guarding a girl named Patty Lowell. The anime is mostly just Dante's miscellaneous adventures but behind the scenes, the Demonic Lord Abigail attempts to once again take over the Human World.
Devil May Cry 2: Dante is given a job by the Protectors from Vie de Marlii to kill the president of a major corporation who is trying to resurrect Argosax the Chaos and gain its power.
Devil May Cry 4: The 4th game stars Nero, a young boy who is part of an Order known as the Order of the Sword. He is sent to hunt Dante down for the Order after the latter killed their leader, but slowly begins to uncover the fact that the Order may have some secrets he wasn't aware of and must help Dante stop them.
Devil May Cry 5: After the events of Devil May Cry 4, the game follows Nero, now with his own branch of Devil May Cry, Dante and his new client, the mysterious V. They must fight off a demon invasion in Red Grave City after a demonic tree takes root and starts to pose a threat to the world.
Power of the verse
Devil May Cry is a rather powerful verse. Most of the Low Tiers of the verse are at least City Block level, scaling to Cerberus, who easily froze Temen-ni-gru's entrance, while Mid Tiers are comfortably in Small City level+ to City level thanks to Echidna's storm feat. The most powerful individuals have Multi-Continent level of power due to Abigail's feat, with God Tiers like Dante, Mundus and Sparda being far superior to him. As for speed, even Low Tiers possess High Hypersonic+ speed via Lady's feat, the Mid Tiers are far faster than her and have Massively Hypersonic+ Combat speed and Reactions by reacting to or moving like Lightning, with the God Tiers being able to easily blitz them.
Note: Please do not try to upgrade the Characters and the Verse to Universal based on Hideki Kamiya's Tweets about Mundus. After much discussion, Universe level Devil May Cry has been rejected and considered unreliable.
Supporters and Opponents of the Verse
The Order of the Sword: